Question

How do you find the standard deviation of a set of numbers?

Answer 1

Population standard deviation:
`sigma = sqrt(((x_1 - bar x)^2+(x_2-bar x)^2+(...)+(x_n-bar x)^2)/n)`

Sample standard deviation:
`s = sqrt(((x_1 - bar x)^2+(x_2-bar x)^2+(...)+(x_n-bar x)^2)/(n-1))`

Explanation:

This is the process to finding the standard deviation for a sample :

Find the mean of the set of numbers: `bar x = (x_1 + x_2 + ... + x_n)/n` where `n =` the number of numbers in the set.

Subtract the mean from each number in your sample, square the difference and add: `(x_1 - bar x)^2+(x_2-bar x)^2+(...)+(x_n-bar x)^2`

Divide these numbers by `n-1` to find the variance of you set. Dividing by `n-1` provides an unbiased sample variance.

Square root the variance to get the standard deviation to the mean:

`s = sqrt(((x_1 - bar x)^2+(x_2-bar x)^2+(...)+(x_n-bar x)^2)/(n-1))`